Phase estimation using phase gradients obtained through Hilbert transform

An algorithm to extract phase in its unwrapped form from an interferogram having perturbed straight line fringes is proposed and studied. Phase gradients are extracted from an interferogram using the Hilbert transform, and the phase is then estimated from their gradients using the method of least squares for the Hudgin geometry. The matrix inversion required in implementing the method of least squares for the Hudgin geometry is carried out analytically by exploiting the additional symmetries available in the Hudgin matrix. The consistency of the proposed algorithm is demonstrated through its implementation, both on numerically generated interferograms, as well as on interferograms measured in a Mach-Zehnder interferometric setup, where the respective imparted phases were random, and corresponded to atmospheric turbulence-like models.